Question

Mr. Williams is driving on a highway at an average speed of 50 miles per hour. His destination is 100 miles away. The

equation d - 100 - 50t gives the distance d (in miles) that he has left to travel as a function of the time t (in hours) that he has
been driving. Write and interpret the inverse of this function (2 points per part).
a. Solve the equation for t by
filling in the empty spaces.
d = 100 - 50
Write the equation.
d-
100 = - 50t
Subtract 100 from both sides.
D-100/-50=t
Divide both sides by -50.
D/-50+2=t
Simplify the left side.
b. Use the inverse function to find the time that Mr. Williams has left to travel when he has driven 75 miles.

Answer 1

t = -d/50 + 2

0.5 hour

Explanation:

Given the equation:

d = 50 - 100t

The inverse function:

A.) solving for t

d = 100 - 50t

d - 100 = - 50t

Divide both sides by - 50

d/-50 - (100/-50) = - 50t/-50

-d/50 - (-2) = t

t = -d/50 + 2

B) using the inverse function:

t = -d/50 + 2

Miles driven (d) = 75, find time (t)

t = - 75/50 + 2

t = - 1.5 + 2

t = 0.5

t is in hours, therefore time left to travel is 0.5 hours or 30 minutes